The Awakening of Faith in the Mahayana is one of my favourite sastras and an important text in Chinese and I assume Vietnamese and Korean (Seeing from Wonhyo's commentary) Buddhism so how is it regarded in Japan?

Zhiyi references it in the Xiao Zhiguan (T46 p467a) - making it important to Tendai.
Honen references it in the Senchakushu - making it important to Jodo Shu.
Shinran quotes it in the Kyogyoshinsho - making it important to Shin Shu.
I'd say it's fairly ubiquitous in Japanese Buddhism.

^A very good article about the intersection of the Mahāyānaśraddhotpādaśāstra & Tiāntāi philosophy (the article also deals with Japanese Tendai). Tiāntāi has traditionally alternatively rejected the Mahāyānaśraddhotpādaśāstra (大乘起信論) or accepted it with considerable reinterpretation and caveats. This article is about some of that reinterpretation, and some of the caveats that were required to make the Mahāyānaśraddhotpādaśāstra acceptable to Tendai Buddhists in Japan, particularly.

The issues Tiāntāi has historically had with the Mahāyānaśraddhotpādaśāstra relate to its Yogācāra/Cittamātra ideology, a perspective critiqued and rejected by Zhiyi, only to have it re-incorporated (controversially, IMO, but I seem to be the only one who thinks this is strange, so take this with a grain of salt) into the teaching under later Tiāntāi patriarchs.

Zhili is the one who tries to incorporate the Mahāyānaśraddhotpādaśāstra into Tiāntāi

^A very good article about the intersection of the Mahāyānaśraddhotpādaśāstra & Tiāntāi philosophy (the article also deals with Japanese Tendai). Tiāntāi has traditionally alternatively rejected the Mahāyānaśraddhotpādaśāstra (大乘起信論) or accepted it with considerable reinterpretation and caveats. This article is about some of that reinterpretation, and some of the caveats that were required to make the Mahāyānaśraddhotpādaśāstra acceptable to Tendai Buddhists in Japan, particularly.

The issues Tiāntāi has historically had with the Mahāyānaśraddhotpādaśāstra relate to its Yogācāra/Cittamātra ideology, a perspective critiqued and rejected by Zhiyi, only to have it re-incorporated (controversially, IMO, but I seem to be the only one who thinks this is strange, so take this with a grain of salt) into the teaching under later Tiāntāi patriarchs.

Zhili is the one who tries to incorporate the Mahāyānaśraddhotpādaśāstra into Tiāntāi

In proofreading the above, a nistake was found: the article linked to does not mentioned Japan, but does mention things that would be/have been relevant to a Japanese Tendai Buddhist, perhaps.

^A very good article about the intersection of the Mahāyānaśraddhotpādaśāstra & Tiāntāi philosophy (the article also deals with Japanese Tendai). Tiāntāi has traditionally alternatively rejected the Mahāyānaśraddhotpādaśāstra (大乘起信論) or accepted it with considerable reinterpretation and caveats. This article is about some of that reinterpretation, and some of the caveats that were required to make the Mahāyānaśraddhotpādaśāstra acceptable to Tendai Buddhists in Japan, particularly.

The issues Tiāntāi has historically had with the Mahāyānaśraddhotpādaśāstra relate to its Yogācāra/Cittamātra ideology, a perspective critiqued and rejected by Zhiyi, only to have it re-incorporated (controversially, IMO, but I seem to be the only one who thinks this is strange, so take this with a grain of salt) into the teaching under later Tiāntāi patriarchs.

Zhili is the one who tries to incorporate the Mahāyānaśraddhotpādaśāstra into Tiāntāi

^A very good article about the intersection of the Mahāyānaśraddhotpādaśāstra & Tiāntāi philosophy (the article also deals with Japanese Tendai). Tiāntāi has traditionally alternatively rejected the Mahāyānaśraddhotpādaśāstra (大乘起信論) or accepted it with considerable reinterpretation and caveats. This article is about some of that reinterpretation, and some of the caveats that were required to make the Mahāyānaśraddhotpādaśāstra acceptable to Tendai Buddhists in Japan, particularly.

The issues Tiāntāi has historically had with the Mahāyānaśraddhotpādaśāstra relate to its Yogācāra/Cittamātra ideology, a perspective critiqued and rejected by Zhiyi, only to have it re-incorporated (controversially, IMO, but I seem to be the only one who thinks this is strange, so take this with a grain of salt) into the teaching under later Tiāntāi patriarchs.

Zhili is the one who tries to incorporate the Mahāyānaśraddhotpādaśāstra into Tiāntāi

Where and why did ZhiYi criticise the Yogacara ideology?

I posted this elsewhere initially but I will paste it here:

n Vasubandhu's theory of consciousness-only, there is only the one consciousness, but it is divided into the discriminating and the undiscriminating forms of consciousness; the discriminating consciousness is what we usually call consciousness, whereas the undiscriminating consciousness is "consciousness appearing to be an object" (sì chén shí / 似塵識). All the physical objects in the universe- vases, clothing, carts, and carriages- are all this undiscriminating form of consciousness.... But since they are all one nature, we can equally say that there are two forms of matter, the disciminating and the undiscriminating.... It is in this sense that the mind and matter are non-dual. Since he [Vasubandhu] is able to say there are these two different forms of consciousness, we can equally say that they are two different forms of matter.... In the Integrated Teaching [Śramaṇa Zhìyǐ's term for what would later be called Tiāntái Buddhism] we can also say that all things are matter only, or sound only, or scent only, or flavour only, or tactile sensation only, or consciousness only. In sum, every dharma inherently mutually possesses all the dharmas through the dharma-realm.

Wait, I need to read the article, Tiantai was influenced by Huayen school, both had criticisms of Yogacarya. This school became the Hosso Consciousness Only in Japan and is basically pretty moribund. Though the current head wrote a great book.

I'll come back and write more but J.Stone Original Enlightenment along with other scholars points out the Japanese hongaku, original enlightenment, thought is different from Awakening of Faith.
gassho
Rory

Namu Kanzeon Bosatsu
Chih-I:
The Tai-ching states "the women in the realms of Mara, Sakra and Brahma all neither abandoned ( their old) bodies nor received (new) bodies. They all received buddhahood with their current bodies (genshin)" Thus these verses state that the dharma nature is like a great ocean. No right or wrong is preached (within it) Ordinary people and sages are equal, without superiority or inferiority
Paul, Groner "The Lotus Sutra in Japanese Culture"eds. Tanabe p. 58https://www.tendai-usa.org/

I'm interested in learning more about this. I don't know much about Yogacara, but have read The Awakening of Faith, mainly for its explanation of the Nine Consciousnesses theory. Is this an idea that began with The Awakening of Faith, and is it specific to Yogacara teaching?

I'm interested in learning more about Madhyamika from the Tiantai perspective. All or most of the available literature seems to come from the Indian and Tibetan traditions, but really I'm only interested in the East Asian Buddhist traditions.

I'm interested in learning more about this. I don't know much about Yogacara, but have read The Awakening of Faith, mainly for its explanation of the Nine Consciousnesses theory. Is this an idea that began with The Awakening of Faith, and is it specific to Yogacara teaching?

I'm interested in learning more about Madhyamika from the Tiantai perspective. All or most of the available literature seems to come from the Indian and Tibetan traditions, but really I'm only interested in the East Asian Buddhist traditions.

Does the text mention 9 specifically? I confess I have still not yet read it. Afaik the 9th consciousness, amalavijñāna is an East Asian development, even in Yogācāra it seems to be Sinitic in origin.

Lastly named spotless consciousness, most extremely pure, tranquil, all unspoiled dharmāḥ supporting, this name applying to consciousness in the Tathāgata state being. Bodhisattva, one of two vehicles, ordinary person, thrones which hold seeds subject to infusion. Yet to acquire the virtuous clean eighth consciousness which is resolute suchness as the sūtra says.

The section quoted is Chapter 3 Section 30 "Names and Types of Eighth Consciousness", so it seems reasonable to potentially infer that East Asian Yogācāra contextualizes the 9th consciousness as some sort of variety of the 8th. The 9th consciousness is Tathāgatagarbha. Non-Sinitic Buddhisms substantiate it to, they just don't happen to formally call it a '9th consciousness' afaik.

On terms of learning Madhyamaka, Ven Zhìyǐ is likely to have learned Madhyamaka in the milieu of figures like Ven Sēngzhào & his teacher Ven Kumārajīva, which would have been, in other words, Indian Madhyamaka. If you are interested in specifically the cultural flavour of easterly teachers' writings as opposed to comparatively westerly ones, then I would suggest trying to find their specific commentarial output. It has to be somewhere. I don't think the Madhyamaka within would differ substantially from any other Madhyamaka of the time, however.

I'm interested in learning more about Madhyamika from the Tiantai perspective.

This is not Tiāntāi, but if this exegesis of the two truths does not at least sympathetically correspond with the 非三而三三而不三 (Not three, they are three; three, they are not three) of Ven Zhìyǐ in my signature atm, I would be surprised.

From Ven Jízàng, whom wikipedia says is considered the founder of East Asian Madhyamaka. Taishō 1854, 二諦義, The Two Truths' Meaning, Scroll 1 @ [0081c28]:

It is time to speak of two truths made of the difference of two views. These two truths equally are missed. How? To those who grasp at existence, sentient beings, speak the absolute truth. To those who grasp at emptiness, sentient beings, speak the relative truth. In this way through is and is not equally sentient beings are grasping. Consequently all misconceive. It is time to speak of two comprehensions which are not two. These two truths equally attained. How? Because these two comprehensions are not two. Two is the principle's teaching. Not two is the teaching's principle. Two is the middle's designation. Not two is the designation's middle. Two is the essence's function. Not two is the function's essence.

It’s been a while since I read it, so maybe it’s only the Ninth/Storehouse Consciousness that it talks about. I don’t know for sure, but isn’t it thought that the text is a Chinese composition? The idea that the Storehouse Conciousness teaching is Sinitic in origin would fit with that, I suppose.

Okay I had time to look into this a bit (only English pubs) and ironically J. Stone's "Original Enlightenment" discusses this. The term "original enlightenment shifted its meaning during Medieval Tendai thought.

The Awakening of Faithclearly takes the former position {awakening means removing afflictions and false views that obstruct one from discerning the buddha nature} , as to a lesser extent, does early Tendai thought. By the medieval period of Tendai history, however, largely under Mikkyo influence, emphasis had shifted heavily in the other direction. All one must do is discern, or even simply have faith in, orignal enlightenment; then the difilements and hindrances appear in their true light as nondual manifestations

Original Enlightenment p. 38.

If you are interested in Japanese Buddhism and intellectual influences this book is really essential.
gassho
Rory

Namu Kanzeon Bosatsu
Chih-I:
The Tai-ching states "the women in the realms of Mara, Sakra and Brahma all neither abandoned ( their old) bodies nor received (new) bodies. They all received buddhahood with their current bodies (genshin)" Thus these verses state that the dharma nature is like a great ocean. No right or wrong is preached (within it) Ordinary people and sages are equal, without superiority or inferiority
Paul, Groner "The Lotus Sutra in Japanese Culture"eds. Tanabe p. 58https://www.tendai-usa.org/